Numbers can be positive, negative, or zero. Positive numbers are greater than zero, and negative numbers are less than zero. You can think of positive and negative numbers as opposites. Positive numbers are used to represent things like money earned, temperatures above zero, or floors above ground level. Negative numbers are used to represent things like debt, temperatures below zero, or floors below ground level.
Negative numbers are written with a minus sign in front of them. For example, -5 is read as 'negative five.' The number line is a useful tool for understanding negative numbers. On a number line, zero is in the middle. Positive numbers go to the right of zero, and negative numbers go to the left. The farther left a number is, the smaller it is. That means -10 is actually less than -3, even though 10 is greater than 3. This is one of the most important rules about negative numbers: the number with the larger absolute value is smaller if both are negative.
Why is -10 less than -3, even though 10 is greater than 3?
The word absolute value appears in the chunk above. The text mentions 'absolute value.' The absolute value of a number is its distance from zero, no matter which direction. What is the absolute value of -7?
Can you think of a real situation where you have seen negative numbers used? For example, weather reports, elevators, or video games?
Integers are the set of whole numbers and their opposites. The set of integers includes ..., -3, -2, -1, 0, 1, 2, 3, ... Zero is an integer, but it is neither positive nor negative. When you add a positive integer, you move to the right on the number line. When you add a negative integer, you move to the left. This is why adding a negative number is the same as subtracting a positive number.
Negative numbers appear in many real-world contexts. In banking, a negative balance means you owe money. In geography, negative elevation means a location is below sea level. The Dead Sea, for example, has an elevation of about -430 meters, meaning it is 430 meters below sea level. In sports, a golf score of -3 means a player is three strokes under par. Understanding negative numbers helps us describe and measure many situations that positive numbers alone cannot capture.
What does a golf score of -3 mean?
Why is zero considered an integer but neither positive nor negative?
The Dead Sea is 430 meters below sea level. If you were standing there, how would you describe your location using negative numbers?